Thanks... I have a quiz on this tomorrow, hopefully he'll leave those types out...
drake... explain the basic to me? AFAIK, this will get me pretty far until I learn more in calc or w/e.
Just the limit as x approaches plus and minus infinity. How you do that, at least how I learned, is about like this:
Basically, you can't evaluate the limit of the function as x approaches infinity because when you plug infinity in, you get infnity/infinity, which is undefined. So, you have to divide the numerator and denominator by the largest power of x.
Edit: This only works if the powers in the denominator are >= those in the numerator. If the numerator's are greater, you're dealing with slant asymptotes.
Easier way to do that limit: L'Hospital's Rule.
Really handy, because it can be applied several times. For example, you want to find the limit of the following function:
So, as a good, easy mneumonic device:
1.) If the exponent of the numerator is greater, the function will have a limit of +infinity or -infinity.
2.) If the exponent of the denominator is greater, the function will have a limit of 0. Series defined by this function will be convergent.
3.) If the exponents of the numerator and denominator are the same, the limit will be a constant of the numerator's greatest-power coefficient times the factorial of the power, divided by the denominator's greatest-power coefficient times the factorial of the power (in the example it was 6*5!/12*5!). I believe that the series will be convergent, but I can't remember for sure.
Also, limits don't need to be taken to infinity. They can be found at any point along the function.
